The Territory of Iowa Was Initially Surveyed in the 1830's

Essay

The Territory of Iowa was initially surveyed in the 1830's. The surveyors were very careful to note the trees and vegetation; it was believed at that time that the richness of the soil could be measured by the density of trees encountered. The sample of hickory tree diameters from the original survey of what is now Linn County, Iowa, is presented in the stem and leaf plot below. The display uses five lines for each stem. Thus, "1t|" is the stem for diameters of 12 and 13, "1f|" for 14 and 15, "1s|" for 16 and 17, and so on. (The "t" then stands for leaves that are twos and threes, the "f" for leaves of fours and fives, etc.)The mean diameter of hickory trees in this sample is 11.849 inches, and the standard deviation is 3.995 inches. ​
(a)What is the approximate diameter of a hickory tree at the 20th percentile in this distribution?
(b)The Empirical Rule would suggest that 68% of hickory tree diameters are between what two values?